Greetings. I was wondering if anyone knew of a way to calculate the efficiency of Newton's Method for a given function: I have an equation f(x) and I'm trying to find a value of x = x0 such that f(x0) = 0. So I start with a guess x0 and then use that to find a second (usually closer) guess of x1 by using the following: x1 = x0 - f(x0)/f'(x0) and then a third guess x2 = x1 - f(x1)/f'(x1) ...and so on until xn = xn-1 +- e, where "e" is some previously defined allowable error. In order to find an "efficiency value" of the above method, I'm thinking this has to do with the rate at which f(x) changes versus the rate at which f"(x) changes. So would I take the derivative of f(x) and divide it by the derivative of f'(x)? = f'(x)/f''(x) .....or would I take the derivative of the entire construct? = [f(x)/f'(x)]' Or are none of these correct?